A self-consistent two-dimensional in coordinate space and three-dimensional in velocity space (2d3v) numerical model based on the particle-in-cell-Monte Carlo collisions technique is developed to study the processes in direct current sputter magnetrons. The model also includes modules for the transport of the sputtered atoms and the gas heating. The main discharge characteristics such as the electrical potential, the density distributions of all plasma species, the gas temperature distribution, and the erosion profile are presented and compared to experimental data, whenever available.